Abstract: The Milnor-Hirzebruch class of a locally complete intersection X in analgebraic manifold M measures the difference between the Poincare dual of theHirzebruch class of the virtual tangent bundle of X and, respectively, theBrasselet-Schuermann-Yokura homology Hirzebruch class of X. In this note, wecalculate the Milnor-Hirzebruch class of a globally defined algebraichypersurface X in terms of the corresponding Hirzebruch invariants of singularstrata in a Whitney stratification of X. Our approach is based on Schuermann-sspecialization property for the motivic Hirzebruch class transformation ofBrasselet-Schuermann-Yokura. The present results also yield calculations ofTodd, Chern and L-type characteristic classes of hypersurfaces.